Question

Write all factors of the following number.
\[60\]

Answer 1

Hint: The given question is about writing all the factors of a given number. Factors are those least numbers which on multiplying with each other and results in getting the same number again. Factors of a given number are obtained by dividing the obtained number again and again with the smallest divisor of that.

Complete step-by-step answer:
The given question is to find out the factors of the given number \[60\] which means we have to write the factors of \[60\]. Factors are nothing but those numbers which on repeatedly get divided by \[60\] and further obtained numbers and hence we get the least numbers. We have to divide the numbers until we are left with \[1\]. The factors obtained on multiplication gives the number back again which is \[60\].
Firstly, we divide \[60\] by \[2\], we are left with \[30\]. Therefore, \[2\] is one factor of \[60\]; on dividing \[60\] by \[2\], we get \[15\], which implies now we get two factors \[2\] and \[3\]. Here, we are left with the number \[15\] after \[2\] divisions. Now, we are left with \[15\]; we have to divide \[15\] by \[2\] but \[15\] is not divisible by \[2\]. Therefore, we have to check the next number which is \[3\]. Now, on dividing \[15\] by \[3\], we get \[5\]. Hence, we get \[3\] factors, \[2,2\] and \[3\]. After division, we are left with \[5\]. Since \[5\] is not divisible by \[3\], we will go to the next number which is \[5\]. So, \[5\] is divided by \[5\] and we get \[1\]. Here, no more factors cannot be found. And we got \[4\] factors as \[2,2,3,5\].
Hence factors of \[60\] are \[2,2,3\] and \[5\].

Note: For example, we have to find out the factors of given numbers \[30\] and hence we get \[2\] factors which are \[2\] and \[15\]. Hence, if we multiply all the \[2\] factors made, we get \[2 \times 15 = 30\]. It means if we multiply the factors of \[30\] and hence, we get \[30\] back.